Chair: Matthijs Koopmans

Abstract: We discuss here conceptual change and the formation of robust learning outcomes from the viewpoint of complex dynamic systems (CDS) [1]. The CDS view considers students? conceptions as context dependent and multifaceted structures which depend on the context of their application [1,2]. In the CDS view the conceptual patterns (i.e. intuitive conceptions here) may be robust in a certain situation but are not formed, at last not as robust ones, in another situation. The stability is then thought to arise dynamically in a variety of ways and not so much mirror rigid ontological categories or static intuitive conceptions as assumed by traditional views on conceptual change. We discuss here a computational model based on CDS, in which the learning process is modelled as a dynamical system in order to study the generic dynamic and emergent features of conceptual change [3]. The model is highly simplified and idealized, but it shows how context dependence, described here through structure of epistemic landscape, leads to formation of context dependent robust states representing learning outcomes, kinds of attractors in learning. Due to sharply defined nature of these states, learning appears as a progression of switch from state to another, giving thus appearance of conceptual change as switch form one robust state to another. These states that correspond the intuitive conceptions of the traditional views, are in CDS, however, dynamical epiphenomena arising from the interaction of learning dynamics and targeted knowledge as coded in the instructional design. Finally, we discuss the implications of the results in guiding attention to the design of the learning task and its structure, and how empirically accessible learning outcomes might be related to these underlying factors. References[1] I. T. Koponen and T. Kokkonen (2014) Frontline Learning Research 4, 140-166.[2] I. T. Koponen (2013) Complexity 19, 27-37.[3] I.T. Koponen, T. Kokkonen and M. Nousiainen (2016) Complexity (in print).

Abstract: Recent methodological developments have shown the applicability of nonlinear frame work (i.e. catastrophe theory, nonlinear time series analysis) in science education research and in relevant psychological theories, such as the neo-Piagetian framework, achievement goal theory or conceptual change theories. In this presentation we are reviewing recent investigations in science education research that concern learning at both, the individual-level and at the group-level processes, which ultimately showed the Complex Dynamic System?s meta-theoretical power. Applications of Catastrophe Theory in problem solving and conceptual understanding in chemistry and physics, opened a new area of investigations by implementing cognitive variables, such as, information processing capacity, logical thinking, field dependence/independence and convergent/ divergent thinking as controls explaining students? achievement [1], [2]. The crucial role of certain factors, acting as bifurcation variables, shed light on phenomena associated with surprising effects and students? failure. The catastrophe theory associates the underling cognitive processes with nonlinear dynamics and self-organization. The nonlinear phenomenology, that is discontinuity in mathematical sense, implies that the leaning outcomes are emergent phenomena [3]. Thus, the complex dynamic systems perspective challenges the existing conceptual change theories, which investigate learning through mechanistic and reductionistic approaches. Analogous investigations applied to cooperative learning settings bring up the issue of learning as an emergent phenomenon resulting from the nonlinear interactions among students working in groups. Students? discourses on explanation of physical phenomena analyzed by orbital decomposition method appeared to possess nonlinear characteristic, which are more pronounced in the more effect sessions [4]. The power law distribution of utterances evolving in time denotes the underlying self-organization processes that lead to the emergent learning outcomes. The merit of the new investigations is three-fold. First, they set the basis of the application of new methods and tools to educational research; second, they have provided rigorous explanations and a better understanding of the phenomena under investigation; and third, they signify a paradigm shift in science education and the rising of the new epistemology that embraces research and practice [3]. References[1] Stamovlasis, D. (2006). The Nonlinear Dynamical Hypothesis in Science Education Problem Solving: A Catastrophe Theory Approach. Nonlinear Dynamics, Psychology and Life Sciences, 10 (1), 37-70.[2] Stamovlasis, D. (2011). Nonlinear dynamics and Neo-Piagetian Theories in Problem solving: Perspectives on a new Epistemology and Theory Development. Nonlinear Dynamics, Psychology and Life Sciences, 15(2), 145-173.[3] Stamovlasis, D. (2016a). Catastrophe Theory: Methodology, Epistemology and Applications in Learning Science. In M. Koopmans and D. Stamovlasis (Eds), Complex Dynamical Systems in Education: Concepts, Methods and Applications (pp. 141-175). Switzerland: Springer Academic Publishing. [4] Stamovlasis, D. (2016b). Nonlinear Dynamical Interaction Patterns in Collaborative Groups: Discourse Analysis with Orbital Decomposition. In M. Koopmans and D. Stamovlasis (Eds), Complex Dynamical Systems in Education: Concepts, Methods and Applications (pp. 273-297). Switzerland: Springer Academic Publishing.

Dimitrios Stamovlasis

28002

Opening the Wondrous World of the Possible for Education: A Generative Complexity Approach.
[abstract]

Abstract: In my contribution, I develop a new more complex view of learning and education. The focus is on opening and enlarging new spaces of the possible around what it means to educate and be educated. To open and enlarge the spaces of the possible for education, new thinking in complexity is needed to describe learning and development as complex processes of generative change. These may facilitate the opening of so-called ?Spaces of Generativity?, as an extension of Vygotsky?s Zone of Proximal Development. Generativity is the very complex human capability of ?knowing how to go on?. These complex spaces are linked to the generative process of learning and development. Learners may achieve their individual and collective generativity through individual and collective activity. Learners may actually co-create and co-generate each other?s learning and development, with potential non-linear, emergent effects. Learning, then, may be viewed as generative, emergent learning. Learners may even bootstrap each other within communities of learners. This may foster the development of the learner as a whole within his/her multi-dimensional Space of Generativity. New thinking in complexity is needed to design education in a new way, by fostering the scaffolding relations among learners. It is through relations that the complexly generative processes of learning and development of these learners can actually be triggered. The quality of these relations determine the quality of interaction and vice versa. The complexity involved may be taken as the fount of new possibilities for education, with effects hitherto unknown. It shows how new thinking in complexity may be taken as foundational for good education, by complexifying education. This complexifying may be viewed as opening the wondrous world of the possible for education. It may show that human beings are able to develop themselves as whole self-realizing human beings through generative processes of becoming. Complexifying education, then, is a way of humanizing education.

Ton Jörg

28003

The Fractal Dynamics of Early Childhood Play, Development and Non-linear Teaching and Learning
[abstract]

Abstract: The Question: How do children before nine years of age actually learn about significant conceptual meanings, solve problems, and develop self-regulation? Educators who care to address this question--and are not content with rote memorization and children who parrot concrete verbalisms--can find some support in considering the dynamic, non-linear processes by which young children learn. Therefore, it makes sense to apprehend how young children learn in order to choreograph and coordinate how to teach in harmonious ways that do no harm. The Response: A complex dynamical systems theory perspective can help to better understand the generative process of early childhood play and learning in human development. It is relevant to envision the non-linearity of sensitive dependence on initial conditions; the equivalence of different surface manifestations with underlying processes; dynamic phase transitions that become a template for? young children's play and learning processes; and their interface with a content-rich, meaning-based dynamic-themes system of curricular implementation.? Throughout the strands of play dynamics, cognitive dynamics, and curricular dynamics, there appear to be similar non-linear dynamical systems functioning within children?s brains. There is discussion of the confluence of research on brain functions; a body or research that informs the characteristics of young children?s play and imagination; and the ways in which young children acquire fresh perceptions and cognitions.? Focus on the spaces among components of physical and interpersonal relationships can illuminate the processes of these non-linear, complex, dynamic systems.

Doris Pronin Fromberg

28004

The Socially Situated Dynamics of Children?s Learning Processes in Classrooms: What do we learn from a Complex Dynamic systems approach?
[abstract]

Abstract: The current literature in educational psychology strongly emphasizes that learners are intentional agents pursuing their personal goals and that they self-regulate their actions in educational contexts. But how do these intentionally regulated learning processes develop over time? The complexity approach in education entails the study of how one condition changes into another, and how the short term and long term time scale of development and learning are interrelated (Van Geert, 1998; Van Geert & Steenbeek, 2005; Thelen & Smith, 1994). Complexity research investigates real-time processes and captures development as it unfolds through multiple interactions between a child and the environment. The approach makes use of microgenetic methods to investigate the interaction between child and environment in real time, and to describe and test its change over time.?But what kind of tools can be used to link these microgenetic measures with long term change ? in processes of learning and skill acquisition - in a meaningful way? In the presentation, we will describe our dynamic interaction model in which teaching-learning processes get their form in the interaction between student and teacher as autonomous, intentional agents. Secondly, several empirical examples will be given in which longitudinal microgenetic measures are combined, such as case studies of the interaction dynamics in student-teacher pairs during individual instruction sessions in arithmetic lessons and during science education (Van der Steen, Steenbeek, Van Dijk, & Van Geert, 2014; Steenbeek, Jansen, van Geert, 2012). In addition, we will discuss state space analysis and other techniques for describing the structure of observational time series as a means to visualize changes in individual teacher-student interaction dynamics, over several time frames. This way the effectiveness of educational interventions can be made visible, in a way that does justice to the complexity and dynamic aspects of the teaching-learning process.

Henderien Steenbeek & Paul van Geert

28005

Using Time Series Analysis to Capture Some Dynamical Aspects of Daily High School Attendance
[abstract]

Abstract: In the United States, high school attendance and drop-out are important policy concerns receiving fairly extensive coverage in the research literature. Traditionally, the focus in this work is on the summary of dropout rates and mean attendance rates in specific schools, regions or socio-economic groups. However, the question how stable those attendance rates are over time has received scant attention. Since such stability may affect how long individual students stay in school, the issue deserves attention. We therefore need to investigate the periodic and aperiodic patterns in students? attendance behavior. The school districts that have begun to keep record of daily attendance rates in their schools over multi-year periods, such as those in New York City, have created an opportunity to do so. This presentation will describe how time series analysis can be used to estimate time sensitive dependencies in daily attendance trajectories, distinguishing random fluctuation therein from cyclical patterns (regularity) and aperiodic ones (unpredictability). After showing simulated examples of each of these three scenarios, I will show their occurrence in the attendance plots of actual schools, based on the attendance trajectories in three schools in the course of the 2013-14 school year (N = 187 in each), and in a fourth one from 2004 to 2011 (N = 1,345). A stepwise modeling process is described to statistically confirm the presence of regular and irregular patterns in the series, and it is illustrated how irregular patterns may suggest self-organized criticality (a tension ? release pattern) in the fourth school.The findings discussed here are meant to address a need in educational research to get a statistical handle on the dynamical processes proposed in the literature, and to illustrate the new insights gained from a temporal perspective on the collection and analysis of educational data in general, school attendance in particular.